A irredutibilidade de polinômios e o teorema de Dumas
This study begins with an overview of numbers, covering from the classification of rational and irrational, to more special categories such as algebraic and transcendent numbers (only conceptual). Our study is aimed at obtaining – in a practical, comprehensive and efficient way – mechanisms that sav...
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| Format: | master thesis |
| Status: | Published version |
| Publication Date: | 2021 |
| Country: | Brasil |
| Institution: | Universidade Federal do Ceará (UFC) |
| Repository: | Repositório Institucional da Universidade Federal do Ceará (UFC) |
| Language: | Portuguese |
| OAI Identifier: | oai:repositorio.ufc.br:riufc/64637 |
| Online Access: | http://www.repositorio.ufc.br/handle/riufc/64637 |
| Access Level: | Open access |
| Keyword: | Raiz racional Polinômios Números irracionais Irredutibilidade (matemática) Rational root Polynomials Irrational numbers Irreducibility (mathematics) |
| Summary: | This study begins with an overview of numbers, covering from the classification of rational and irrational, to more special categories such as algebraic and transcendent numbers (only conceptual). Our study is aimed at obtaining – in a practical, comprehensive and efficient way – mechanisms that save us time when it is necessary to classify a certain number in the set of reals. It is in this context that we focus our study, associating a given real number to the root of a polynomial – from which we have the idea of irreducibility linked to the irrationality of a number – and then we can decompose it as a product of polynomials. Thus, we present the methods – Rational Roots Theorem, Eisenstein Criterion and Dumas Criterion – commonly used to assess whether a given polynomial has rational roots or not. |
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